Unclear differential equation from a thermodynamics textbook

NODARman
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In the thermodynamics textbook there is written: 𝛿𝐴 = 𝑇𝑑𝑆 βˆ’ π‘‘π‘ˆ = 𝑑(𝑇𝑆) βˆ’ 𝑆𝑑𝑇 βˆ’ π‘‘π‘ˆ = βˆ’π‘‘(π‘ˆ βˆ’ 𝑇𝑆) βˆ’ 𝑆𝑑𝑇 = βˆ’π‘‘πΉ βˆ’ 𝑆𝑑𝑇
How did we get the bolded area from TdS? Is that property of derivative, integral, or something else :/
 
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Product rule
 
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Sorry for being so terse. I was posting from my phone.

Apply the product rule to ##TS##. ##d(TS) = ?##.
 

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